Question: A circle with area $64\pi$ has a sector with a $\dfrac{5}{6}\pi$ radian central angle. What is the area of the sector? ${64\pi}$ $\color{#9D38BD}{\dfrac{5}{6}\pi}$ ${\dfrac{80}{3}\pi}$
The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{5}{6}\pi \div 2 \pi = \dfrac{A_s}{64\pi}$ $\dfrac{5}{12} = \dfrac{A_s}{64\pi}$ $\dfrac{5}{12} \times 64\pi = A_s$ $\dfrac{80}{3}\pi = A_s$